find the measure of an interior and an exterior angle of a regular 46-gon ?

Question

find the measure of an interior and an exterior angle of a regular 46-gon ?

Answer 1

Nearly 50 years ago Seymour Papert and a team from MIT invented Turtle Graphics (which became the Logo computer programming language) using a computer-controlled “turtle” to draw on the floor.  Today, Turtle Graphics (Logo) can be accessed online and in Microsoft’s free Small Basic.

Let’s say that the Turtle is pointing to the right and will go around the polygon in a counter-clockwise manner.  For a regular 46-gon, the Turtle gets these commands 46 times:

       MOVE 1

       LEFT (360/46) DEGREES

And it ends up at the beginning spot pointing to the right.

 

The amount of each turn, the exterior angle, is 360/46 (=7.8) degreeswhich means that the sum of the external angles of the polygon is 360 degrees (a complete turn).

 

And, since the interior angle is (180 degrees – exterior angle), a straight line modified by that much, the interior angle of a 46-gon is:

     180 – (360/46)

     (46*180 – 360) / 46

    (8280 – 360) / 46

     172.2 degrees

 

The general rule for the interior angle of a regular polygon is:  (n-2)*180/n.

 

Answer 2

Julie, the interior angles total 360 degrees, so 46 would each be 360/46 = 7.83 degrees.

 

The exterior angles are supplementary to the interior angles. 180 - 7.83 = 172.17 degrees.